How many different 8 letter words are possible using the letters of the word SYLLABUS?

Explanation

Count the letters in SYLLABUS: S-Y-L-L-A-B-U-S has 8 letters total. Notice that S appears 2 times and L appears 2 times. These repeated letters need special treatment in counting arrangements.

If all 8 letters were different, there would be 8 factorial arrangements. But since S repeats twice, we divide by 2 factorial. Since L also repeats twice, we divide by another 2 factorial to avoid counting duplicates.

The formula is 8 factorial divided by 2 factorial times 2 factorial. This equals 40,320 divided by 2 times 2, which equals 40,320 divided by 4, giving 10,080 different words.